Error-floor mitigation of layered decoders using non-standard layered-decoding schedules

ABSTRACT

A layered decoder that uses a non-standard schedule, where a non-standard schedule is a schedule where the frequency of one or more layers in the schedule is greater than one. When the layered decoder converges on a near codeword using an initial schedule, the layered decoder identifies the layer L maxb  of the near codeword, which layer contains the greatest number of unsatisfied check nodes, and selects a subsequent non-standard schedule from a schedule set. The non-standard schedules in the schedule set are sorted by key layer, where the key layer is a layer that appears in the non-standard schedule with the greatest frequency. The layer decoder selects a non-standard schedule from the schedule set where the key layer of selected non-standard schedule is equal to the identified L maxb  value.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of the filing date of U.S.provisional application No. 61/089,297, filed on Aug. 15, 2008 asattorney docket no. 08-0241-PR, the teachings of which are incorporatedherein by reference in their entirety.

The subject matter of this application is related to (1) the subjectmatter of U.S. application Ser. No. 12/420,535 filed on Apr. 8, 2009 asattorney docket number 08-0242, (2) the subject matter of U.S.application Ser. No. 12/333,840 filed on Dec. 12, 2008 as attorneydocket number 08-0324, (3) the subject matter of PCT application no.PCT/US08/86523 filed on Dec. 12, 2008 as attorney docket no. 08-0241,(4) the subject matter of PCT application no. PCT/US08/86537 filed onDec. 12, 2008 as attorney docket no. 08-1293, (5) the subject matter ofPCT application no. PCT/US09/39918 filed on Apr. 8, 2009 as attorneydocket number 08-0243, (6) the subject matter of U.S. application Ser.No. 12/401,116 filed on Mar. 10, 2009 as attorney docket number 08-0248,(7) the subject matter of U.S. application Ser. No. 12/475,786 filed onJun. 1, 2009 as attorney docket number 08-0250, (8) the subject matterof U.S. application Ser. No. 12/260,608 filed on Oct. 29, 2009 asattorney docket number 126803, (9) the subject matter of PCT applicationno. PCT/US09/41215 filed on Apr. 21, 2009 as attorney docket number126782, (10) the subject matter of PCT application no. PCT/US09/39279filed on Apr. 2, 2009 as attorney docket number 08-1057, (11) thesubject matter of U.S. application Ser. No. 12/323,626 filed on Nov. 26,2008 as attorney docket number Graef 26, (12) the subject matter of U.S.application Ser. No. 12/427,786 filed on Apr. 22, 2009 as attorneydocket number Graef 27, (13) the subject matter of US application no.U.S. Ser. No. 12/492,328 filed on Jun. 26, 2009 as attorney docketnumber 08-0242A, (14) the subject matter of U.S. application Ser. No.12/492,346 filed on Jun. 26, 2009 as attorney docket number 08-0242B,(15) the subject matter of U.S. application Ser. No. 12/492,357 filed onJun. 26, 2009 as attorney docket number 08-0242C, (16) the subjectmatter of U.S. application Ser. No. 12/492,374 filed on Jun. 26, 2009 asattorney docket number 08-0242D, (17) the subject matter of US patentno. 2008/0276156 published on Nov. 6, 2008, (18) the subject matter ofUS patent no. 2008/0301521 published on Dec. 4, 2008, (19) the subjectmatter of U.S. application Ser. No. ______ filed on the same day as thisapplication as attorney docket number 08-0244, and (20) the subjectmatter of U.S. application Ser. No. ______ filed on the same day as thisapplication as attorney docket number 09-0432, the teachings of whichare incorporated herein by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to digital signal processing, and, in particular,to data-encoding methods such as low-density parity check (LDPC) coding.

2. Description of the Related Art

Communication is the transmission of information from a transmitter to areceiver over a communications channel. In the real world, thecommunications channel is a noisy channel, providing to the receiver adistorted version of the information transmitted from the transmitter. Astorage device (e.g., hard disk (HD) drive, flash drive) is one suchnoisy channel, accepting information from a transmitter, storing thatinformation, and then providing a more or less distorted version of thatinformation to a receiver.

The distortion introduced by a communications channel such as a storagedevice might be great enough to cause a channel error, i.e., where thereceiver interprets the channel output signal as a 1 when the channelinput signal was a 0, or vice versa. Channel errors reduce throughputand are thus undesirable. Hence, there is an ongoing need for tools thatdetect and/or correct channel errors. Low-density parity check (LDPC)coding is one method for the detection and correction of channel errors.

LDPC codes are among the known near-Shannon-limit codes that can achievevery low bit-error rates (BER) for low signal-to-noise ratio (SNR)applications. LDPC decoding is distinguished by its potential forparallelization, low implementation complexity, low decoding latency, aswell as less-severe error floors at high SNRs. LDPC codes are consideredfor virtually all the next-generation communication standards.

SUMMARY OF THE INVENTION

A decoder-implemented method for decoding a decoder input codeword,where the method selects a decoding schedule for layered decoding, wherethe layered decoding corresponds to a code having two or more layers,and at least one layer in the code appears more than once in theselected decoding schedule. The method performs the layered decoding onthe decoder input codeword using the selected decoding schedule.

A decoder for decoding a decoder input codeword, where the decoderselects a decoding schedule for layered decoding, where the layereddecoding corresponds to a code having two or more layers, and at leastone layer in the code appears more than once in the selected decodingschedule. The decoder performs the layered decoding on the decoder inputcodeword using the selected decoding schedule.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, features, and advantages of the invention will becomemore fully apparent from the following detailed description, theappended claims, and the accompanying drawings in which like referencenumerals identify similar or identical elements.

FIG. 1 is a block diagram of a communications system 100 that utilizesLDPC coding.

FIG. 2(A) depicts LDPC H matrix 200, and FIG. 2(B) is a Tanner graph ofH matrix 200.

FIG. 3 is a flowchart of non-layered LDPC-decoding method 300 used bydecoder 114 of FIG. 1.

FIG. 4 is a flowchart of a layered LDPC-decoding process 400 executed bydecoder 114 of FIG. 1.

FIG. 5 is a block diagram of layered-decoding system 500.

FIG. 6 is a flowchart of a layered-decoding process 600 that may beexecuted by layered decoder 502 of system 500.

FIG. 7 is a block diagram of a portion of offline schedule-testingsystem 700.

FIG. 8 is a flowchart of offline schedule-testing process 800 executedby simulated layered decoder 704 in system 700 of FIG. 7.

FIG. 9 is a flowchart of offline schedule-testing process 900 executedby simulated layered decoder 704 of system 700 of FIG. 7, wherein theschedules in schedule population 706 are schedules with an associatedkey-layer value, according to various embodiments of the presentinvention.

FIG. 10 is a flow diagram of a layered-decoding method 1000 executed bylayered decoder 502 in production layered-decoding system 500 accordingto various embodiments of the present invention.

DETAILED DESCRIPTION

FIG. 1 is a block diagram of a communications system 100 that utilizesLDPC coding. Data source 102 generates a set of bits known as anoriginal information word 104. LDPC encoder 106 encodes originalinformation word 104 to generate original encoded codeword 108. LDPCencoding is discussed in greater detail below. Original encoded codeword108 (also known as the channel input codeword) is written to storagemedium 110 (e.g., a flash drive, hard-drive platter, etc) as a writtenencoded codeword.

At some later time, storage medium 110 provides the written encodedcodeword as a set of values y (i.e., a channel output codeword) tochannel detector 112. Channel detector 112 converts the received valuesy into a set of log-likelihood ratio (LLR) values L_(ch). An LLR valuecomprises (i) a sign bit that represents the receiver's best guess as tothe one-bit hard-decision value indicated by the corresponding value yand (ii) one or more magnitude bits that represent the receiver'sconfidence in the hard decision. For example, channel detector 112 mightoutput each LLR value L_(ch) as a five-bit value, where themost-significant bit is a sign bit that indicates the hard decision, andthe value of the four magnitude bits indicates the confidence of thehard decision. Thus, in one possible LLR scheme, an LLR value of binary00000 indicates a hard decision of 0 with least confidence, an LLR valueof binary 01111 indicates a hard decision of 0 with maximum confidence,an LLR value of binary 10001 indicates a hard decision of 1 with leastconfidence, and an LLR value of binary 11111 would indicate a harddecision of 1 with maximum confidence, where binary 10000 is unused.

Channel detector 112 sends sets of L_(ch) values to LDPC decoder 114 asdecoder input codewords. LDPC decoder 114 performs one or more localdecoding iterations 116 on each set of L_(ch) values to generate adecoded codeword {circumflex over (x)}. LDPC decoder 114 terminates wheneither (i) LDPC decoder 114 arrives at a decoded correct codeword(DCCW), i.e., {circumflex over (x)} is the same as channel inputcodeword 108, or (ii) LDPC decoder 114 performs a maximum allowablenumber of local iterations without arriving at the DCCW, i.e., LDPCdecoder 114 has failed. When decoder 114 terminates, it outputs decodedcodeword {circumflex over (x)} to data destination 118. LDPC decoding isdescribed in greater detail below.

Channel controller 120 controls the operations of one or more of LDPCencoder 106, channel detector 112, and LDPC decoder 114. The channelcontroller is typically an ARM (Advanced RISC (reduced instruction-setcode) Machine) processor.

LDPC Encoding

To create codeword 108, LDPC encoder 106 appends to the bits ofinformation word 104 a number of parity bits specified by the LDPC code.The number of bits in information word 104 is denoted K. The bits in anencoded codeword are known as variable bits, and the number of thosevariable bits is denoted N. Thus, the number of parity bits is given byN−K.

Each parity bit in an LDPC codeword is associated with one or more otherbits in that codeword in a particular way as specified by the particularLDPC code, and the value assigned to a parity bit is set so as tosatisfy the LDPC code. Typical LDPC codes specify that the parity bitand its associated bits satisfy a parity-check constraint, e.g., the sumof the bits is an even number, i.e., sum modulo 2=0.

The LDPC Code

A particular LDPC code is defined by a two-dimensional matrix of 1s and0s known as the parity-check matrix, or H matrix, or simply H. H isknown, a priori, by both the LDPC encoder and decoder. H comprises Ncolumns and N−K rows, i.e., a column for every bit of the codeword, anda row for every parity bit. Each 1 in H represents an associationbetween the codeword bit of the column and the parity bit of the row.For example, a 1 at the third row, seventh column of H means that thethird parity-check bit is associated with the seventh bit of thecodeword. The sum modulo 2 of the value of a check bit and all variablebits associated with that check bit should be 0. A definingcharacteristic of typical LDPC codes is that H is “sparse,” i.e., theelements of H are mostly 0s with relatively few 1s.

FIG. 2(A) depicts LDPC H matrix 200. H matrix 200 comprises N=9 columnsand N−K=6 rows. Thus, H matrix 200 defines an LDPC code that accepts athree-bit information word, appends six parity bits, and outputs anine-bit codeword. In one implementation in which the storage medium isa hard-disk drive or a flash drive, each information word is 4,096 bitsin length, and each codeword is 4,552 bits in length. Otherimplementations may have information words and/or codewords having otherbit lengths.

LDPC Decoding: Belief Propagation

FIG. 3 is a flowchart of non-layered LDPC-decoding method 300 used bydecoder 114 of FIG. 1. The heart of decoding method 300 is an iterative,two-phase message-passing algorithm called belief propagation. Beliefpropagation can be explained with the use of a Tanner graph.

FIG. 2(B) is a Tanner graph for H matrix 200. In general, a Tanner graphcomprises 1) a number of bit nodes (also known as variable nodes) nequal to the number of columns in H (and thus equal to the number N ofvariable bits, 2) a number of check nodes m equal to the number of rowsin H (and thus equal to number of parity bits), 3) edges 202, each ofwhich connects a single bit node n_(i) to a single check node m_(j), 4)for each bit node n_(i), the original L_(ch) value, and 5) for each bitnode n_(i), a calculated hard-decision output value {circumflex over(x)}_(n). The Tanner graph of FIG. 2(B) comprises nine bit nodes n₀-n₈,six check nodes m₀-m₅, 18 edges 202 connecting bit nodes to check nodes,nine L_(ch) values, and nine {circumflex over (x)}_(n) values.

The edges in a Tanner graph represent the relationships between bitnodes n and check nodes m, where edges represent 1s in H. For example,in FIG. 2(B), an edge 202 connects first bit node n₀ to fourth checknode m₃, because there is a 1 in the first column, fourth row of Hmatrix 200 in FIG. 2(A).

A Tanner graph is a bipartite graph, i.e., an edge can connect a bitnode to only a check node, and cannot connect a bit node to another bitnode, or a check node to another check node. The set of all bit nodes nconnected by edges to a particular check node m is denoted N(m). The setof all check nodes m connected by edges to a particular bit node n isdenoted M(n). The index of a particular (bit or check) node is itsordinal sequence in the graph.

Returning to FIG. 3, processing starts at step 302 and proceeds to step304, decoder initialization. Decoder initialization 304 comprisessetting all edges (e.g., edges 202 of FIG. 2(B)) connected to each bitnode n to the corresponding L_(ch) value associated with bit node n, andsetting the {circumflex over (x)}_(n) value of bit node n to thehard-decision value (i.e., MSB) of bit node n's L_(ch). Thus, forexample, in FIG. 2(B), if the L_(ch) value associated with bit node n₀is the decimal value +5, then, at step 304, the two edges 202 connectingbit node n₀ to check nodes m₀ and m₃ are set to +5, and bit node n₀ 's{circumflex over (x)}_(n) value is set to 1. An alternative way ofexpressing the first part of this step is that bit node n₀ sends amessage of +5 to each check node m in set M(n₀). A message sent from abit node n to a check node m is called a bit-node message or Q message,and is denoted Q_(mn).

Step 304 then sends to syndrome check 306 a candidate decoded codewordvector {circumflex over (x)} comprising the N {circumflex over (x)}_(n)values. Syndrome check 306 calculates syndrome vector z using thefollowing Equation (1):

z={circumflex over (x)}H^(T)   (1)

where H^(T) is the transpose of the H matrix. If syndrome vector z is a0 vector, then vector {circumflex over (x)} has satisfied all theparity-check constraints defined by H, i.e., {circumflex over (x)} is avalid decoded codeword. In that case, processing proceeds tocyclic-redundancy check (CRC) 308 (discussed below).

If, instead, syndrome vector z is not a 0 vector, then vector{circumflex over (x)} fails one or more of the parity-check constraints.Each non-zero element in syndrome vector z represents a failedparity-check constraint, which is also referred to as unsatisfied checknode (USC). A USC is a check node associated with an odd number oferroneous bit nodes (“EBNs”). The number of non-zero elements insyndrome vector z is the number b of USCs in vector {circumflex over(x)}. Further, the indices of the non-zero elements of syndrome vector zare the indices of the USCs in vector {circumflex over (x)}.

If vector {circumflex over (x)} fails syndrome check 306, thenprocessing continues to the first of one or more decoding iterations 310(called “local decoding iterations”). Local decoding iteration 310comprises three steps: 1) a belief-propagation check-node update 312, 2)a belief-propagation bit-node update 314, and 3) a syndrome check 316,which is identical to syndrome check 306.

In belief-propagation check-node update 312, each check node m uses theQ_(nm) messages received from all bit nodes n in set N(m) to calculateone or more check-node messages or R messages, denoted R_(mn), accordingto the following Equations (2), (3), and (4):

$\begin{matrix}{R_{mn}^{(i)} = {\delta_{mn}^{(i)}{\max \left( {{\kappa_{mn}^{(i)} - \beta},0} \right)}}} & (2) \\{\kappa_{mn}^{(i)} = {{R_{mn}^{(i)}} = {\min\limits_{n^{\prime} \in {{N{(m)}}\backslash \; n}}{Q_{n^{\prime}m}^{({i - 1})}}}}} & (3) \\{\delta_{mn}^{(i)} = \left( {\prod\limits_{n^{\prime} \in {{N{(m)}}\backslash \; n}}\; {{sgn}\left( Q_{n^{\prime}m}^{({i - 1})} \right)}} \right)} & (4)\end{matrix}$

where i is the decoding iteration, N(m)\n is set N(m) excluding bit noden, the function sgn returns the sign of its operand, and β is a positiveconstant, the value of which depends on the code parameters. Each checknode m sends the calculated R_(mn) messages back along those same edgesto all bit nodes n in set N(m).

Next, in belief-propagation bit-node update 314, each bit node ncalculates one or more Q_(nm) messages according to the followingEquation (5):

$\begin{matrix}{Q_{n\; m}^{(i)} = {L_{n}^{(0)} + {\sum\limits_{m^{\prime} \in {{M{(n)}}\backslash m}}R_{m^{\prime}n}^{(i)}}}} & (5)\end{matrix}$

where L_(n) ⁽⁰⁾ is the original L_(ch) value for bit node n, and M(n)\mis set M(n) excluding check node m. Each bit node n then sends thecalculated Q_(nm) messages to all check nodes m in set M(n).

Also during bit-node update 314, each bit node n updates its {circumflexover (x)}_(n) value according to the following Equations (6) and (7):

$\begin{matrix}{E_{n}^{(i)} = {\sum\limits_{m^{\prime} \in {M{(n)}}}R_{m^{\prime}n}^{(i)}}} & (6) \\{P_{n} = {L_{n}^{(0)} + E_{n}^{(i)}}} & (7)\end{matrix}$

If P_(n)≧0, then {circumflex over (x)}_(n)=0, and if P_(n)<0, then{circumflex over (x)}_(n)=1. The values generated by Equation (6) arealso referred to as extrinsic or E values, and denoted E_(LDPC). Thevalues generated by Equation (7) are referred to as P values. Thespecific belief-propagation algorithm represented by Equations (2)-(7)is known as the min-sum algorithm. Note that the {circumflex over(x)}_(n) values are updated during each local decoding iteration 310 andfinally outputted by decoding process 300. The original LLR valuesL_(ch) remain unchanged during decoding process 300.

Bit-node update 314 sends to syndrome check 316 a vector {circumflexover (x)} constructed out of the current {circumflex over (x)}_(n)values of the decoder. If vector {circumflex over (x)} passes syndromecheck 316, then vector {circumflex over (x)} is sent to CRC 308.

LDPC Decoding: Cyclic Redundancy Check and Mis-Satisfied Check Nodes

Passing syndrome check 306 or 316 means that vector {circumflex over(x)} is a valid decoded codeword, but not necessarily the decodedcorrect codeword (DCCW). It is possible for an LDPC decoder to generatea valid decoded codeword that is not the DCCW. In that case, there areno USCs in vector {circumflex over (x)}, but there are mis-satisfiedcheck nodes (MSCs). A mis-satisfied check node is a check node that isassociated with an even number of erroneous bit nodes (EBNs).

Thus, to ensure that valid vector {circumflex over (x)} is the DCCW,process 300 passes vector {circumflex over (x)} to cyclic redundancycheck (CRC) 308. A CRC check is a checksum operation that can detectalteration of data during transmission or storage. Specifically, anencoder (e.g., encoder 106 of FIG. 1) computes a first CRC checksum of acodeword that is to be sent, and sends both the first CRC checksum andthe codeword to the decoder. The decoder, upon receipt of the codewordand the first CRC checksum, computes a second CRC checksum using thedecoded codeword, and compares the second checksum to the first CRCchecksum. If the two CRC checksums do not match, then there are errorsin the decoded codeword.

If vector {circumflex over (x)} passes CRC check 308, then vector{circumflex over (x)} is the DCCW, and process 300 sets global variableDCCW to true, outputs vector {circumflex over (x)}, and terminates atstep 320. Otherwise, vector {circumflex over (x)} is not the DCCW, andprocess 300 sets global variable DCCW to false, outputs vector{circumflex over (x)}, and terminates at step 320. Global variable DCCWinforms other decoding processes whether or not the DCCW has beengenerated.

Returning to syndrome check 316, if vector {circumflex over (x)} failsthe syndrome check, then there exist one or more USCs in vector{circumflex over (x)}. The typical method for resolving USCs is toperform another local decoding iteration 310. However, in a particulardecoding session, there might exist one or more USCs that will never besatisfied in a reasonable amount of time (see the discussion of trappingsets, below). Thus, LDPC decoders are typically limited in how manylocal decoding iterations they perform. Typical values for the maximumnumber of iterations range from 50 to 200.

In FIG. 3, step 318 determines whether the specified maximum number oflocal decoding iterations has been reached. If not, then another localdecoding iteration 310 is performed. If, instead, the maximum number oflocal decoding iterations has been reached, then decoder process 300 hasfailed. In that case, process 300 sets global variable DCCW to false,outputs vector {circumflex over (x)}, and terminates at step 320.

A complete execution of process 300 (with one or more local decodingiterations 310) is known as a local decoding session.

Layered Decoding and Decoding Schedules

A layer is a subset of check nodes. A typical layer is a subset of checknodes, i.e., rows of an H matrix, that have no bit nodes in common.Layers are numbered beginning with 0; thus, a four-layer H matrixcomprises layers 0, 1, 2, and 3. For example, H matrix 200 in FIG. 2(A)may be decomposed into two sub-graphs corresponding to two layers, where(i) the first layer (layer 0) includes the first three check nodes(i.e., the first, second, and third rows in H matrix 200), which do notupdate common bit nodes, and (ii) the second layer (layer 1) includesthe last three check nodes (i.e., the fourth, fifth, and sixth rows in Hmatrix 200), which also do not update common bit nodes.

LDPC decoding can be layered or non-layered. In non-layered decoding(e.g., decoding process 300 of FIG. 3), a local decoding iteration hasthree steps: (i) a single check-node update (e.g., step 312 of FIG. 3)of all check nodes in the codeword, (ii) a single bit-node update (e.g.,step 314 of FIG. 3) of all bit nodes in the codeword, and (iii) asyndrome check (e.g., step 316 of FIG. 3) of the entire codeword.

In layered decoding, a local-decoding iteration comprises two or moredecoding sub-iterations, wherein each decoding sub-iteration comprises(i) a check-node update of a different layer of the H matrix, (ii) abit-node update of that layer, (iii) a syndrome check of that layer, and(iv) a convergence check of the decoder codeword.

The sequence in which layers are processed by a layered decoder isdetermined by a decoding schedule. For example, for an H matrix havingthree layers (i.e., layers 0, 1, and 2), a schedule of [1,0,2] impliesthat the layered decoder decodes using layer 1 first, layer 0 second,and layer 2 third. If, after layer 2, the layered decoder has notgenerated the DCCW, then the sequence is re-initiated.

As used herein, the term “decoding schedule” (or alternatively“schedule”) refers a layer sequence that cannot be decomposed into twoor more iterations of another layer sequence. For example, [0,1,2] is aschedule, but [0,1,2,0,1,2] is not a proper schedule because it iscomposed of two iterations of the layer sequence [0,1,2]. Note, further,that [0,1,2,0,1,2,0] is a proper schedule. Although it contains twoinstances of the layer sequence [0,1,2], it cannot be decomposed intoonly those two instances due to the existence of the third instance oflayer 0.

FIG. 4 is a flowchart of a layered LDPC-decoding process 400 executed bydecoder 114 of FIG. 1. The sequence in which layers are decoded byprocess 400 is specified by a schedule (not shown). Steps 402, 404, 406,418, 408, and 420 of process 400 are analogous to steps 302, 304, 306,318, 308, and 320 of FIG. 300.

Local decoding iteration 410 of process 400 is analogous to localdecoding iteration 300 of FIG. 3 in that both local decoding iterationscorrespond to a single, complete pass through the corresponding Hmatrix. For local decoding iteration 300, a complete pass corresponds toa single update of each check node and bit node and a correspondingsyndrome check. For local decoding iteration 410, a complete passcorresponds to a single implementation of the entire schedule associatedwith the layered decoder, where each layer in the schedule involvesupdating the check nodes and bit nodes associated with that layer and acorresponding layer syndrome check and convergence check.

Local decoding iteration 410 begins at step 422 with the selection ofthe first/next layer in the schedule. Sub-iteration 430 is thenperformed for the selected layer. In particular, at step 412, acheck-node update is performed on the check nodes of the selected layer.The check-node update process of step 412 is analogous to the check-nodeupdate process of step 312 of FIG. 3. Next, at step 414, a bit-nodeupdate is performed on all bit nodes associated with the check nodesbelonging to the selected layer. The bit-node update process of step 414is analogous to the bit-node update process of step 314 of FIG. 3.

Next, at step 416, a syndrome check is performed on the selected layer.If the selected layer fails layer syndrome check 416, then processingcontinues to step 426; otherwise, processing continues to convergencecheck 424. To pass convergence check 424, (i) no layer in the codewordcan have any USCs and (ii) all layers in the codeword must be stable,i.e., for each layer, no bit node changed value during the most-recentperformance of step 414 on that layer. If convergence check 424 passes,then process 400 continues to CRC check 408; otherwise, control passesto step 426, where it is determined if there is another layer in theschedule. If so, then processing returns to step 422 to select the nextlayer in the schedule and perform another sub-iteration 430 with thatnext layer. Otherwise, processing passes to step 418.

The bit-error rate (BER) of an LDPC decoder represents the probabilitythat a decoded bit has the wrong value. Thus, for example, a decoderwith a BER of 10⁻⁹ will, on average, generate one erroneous bit forevery billion decoded bits. The failure of an LDPC decoding session toconverge on the DCCW contributes to the BER of the decoder.

The BER of an LDPC decoder is strongly influenced by the signal-to-noiseratio (SNR) of the decoder's input signal. A graph of BER as a functionof SNR typically comprises two distinct regions: an initial “waterfall”region where the BER improves (decreases) rapidly given a unit increasein SNR, and a subsequent “error-floor” region where increases in SNRyield only modest improvements in BER. Thus, achieving significant BERimprovements in the error-floor region requires methods other than SNRincrease.

In a typical LDPC-decoding session, the decoder converges on the DCCWwithin the first several local decoding iterations. When, instead, anLDPC decoder fails to converge on the DCCW within the specified maximumnumber of iterations, the LDPC decoder is known as a failed decoder, andthe decoded codeword generated by a failed decoder is a failed codeword.

Failed codewords typically are classified by the number b of USC nodesthey contain. An invalid decoded codeword (ICW) is a failed codewordwith a large b value (e.g., greater than 16 for an approximately5,000-bit codeword). ICWs typically result from a decoder input codewordthat contains so many bit errors, i.e., so few correct values, that thedecoder is unable to correct all the bit errors. A typicalpost-processing method for handling an ICW is to request a re-send ofthe input codeword.

A near codeword (NCW) is a failed codeword that possesses a small bvalue (e.g., 16 or fewer for an approximately 5,000-bit codeword).Sometimes, the USCs, EBNs, and MSCs in an NCW form a stableconfiguration, known as a trapping set, for which further local decodingiterations will not produce the DCCW. The majority of trapping setscomprise fewer than five USCs and fewer than ten EBNs. A trapping setmight have no USCs, i.e., the trapping set might be composed solely ofMSCs and their associated EBNs.

Trapping sets have a significant impact on the error-floorcharacteristics of an LDPC decoder, i.e., when a decoder fails in theerror-floor region, the failure is typically due to a trapping set.Changing one or more parameters of a local decoding session (e.g., EBNvalues, check-node update methods, etc.) and performing further decodingmight result in the decoder converging on the DCCW. When successful,this process is referred to as breaking the trapping set.

A typical layered decoder is not limited to using the same schedule forevery local decoding iteration, but can be reconfigured with a differentschedule at any time, e.g., between local decoding iterations. Changingthe schedule of a layered decoder and re-performing decoding can break atrapping set. For example, if a four-layer decoder with a schedule of[0,1,2,3] fails with an NCW that contains a trapping set, thenreconfiguring the decoder with another schedule, e.g., [0,2,1,3] andre-performing decoding might break the trapping set.

According to certain embodiments of the present invention, there is notheoretical limitation on the length of a schedule, the sequence oflayers in a schedule, or on the number of times a particular layerappears in a schedule, also known as the frequency of the layer, whereinthe frequency of a layer is one or greater. Hence, there are an infinitenumber of possible schedules for any given layered decoder. For example,a five-layer decoder can have the schedule [4,1,0,2,3], or the schedule[0,4,0,1,3,2,4,2,4,4,2]. In the first schedule, all layers have afrequency of one. In the second schedule, layers 1 and 3 have afrequency of one, layer 0 has a frequency of two, layer 2 has afrequency of three, and layer 4 has a frequency of four.

Although there are an infinite number of possible schedules, prior-artlayered decoders use only schedules where each layer is decoded once(i.e., where each layer has a frequency of one), also known as standardschedules. Thus, for a five-layer decoder, [0,1,2,3,4], [4,3,2,1,0], and[4,0,1,3,2] are three possible standard schedules. A typical layereddecoder uses the same standard schedule, i.e., a default schedule, forthe initial decoding of every codeword.

There exist n! different standard schedules for an n-layer code.Accordingly, for a particular n-layer decoder, the universe of possibleschedules can be divided into two sets: a first set containing n!standard schedules, and a second set containing an infinite number ofnon-standard schedules. A non-standard schedule is a schedule where oneor more layers occur with a frequency greater than one.

It is possible to implement a layered decoder with a schedule memorythat stores a schedule set of one or more schedules for the layereddecoder. Such a schedule set stored in a schedule memory may be referredto as a decoding-schedule database. If the layered decoder fails toconverge on the DCCW using a particular schedule, then the layereddecoder can select a different schedule from the schedule set andre-perform decoding using that different schedule. This process isrepeated until either (i) the layered decoder converges on the DCCW or(ii) all schedules in the schedule memory have been used.

FIG. 5 is a block diagram of layered-decoding system 500. System 500comprises layered decoder 502 and schedule memory 504. The layereddecoder is connected to the schedule memory. The schedule memory storesa schedule set 506. In a typical implementation, schedule set 506 is adata structure, e.g., a table, comprising a single column (field).Schedule set 506 comprises any number of rows (records) wherein each rowidentifies a single schedule.

FIG. 6 is a flowchart of a layered-decoding process 600 that may beexecuted by layered decoder 502 of system 500. Processing begins at step602 and proceeds to step 604 where layered decoder 502 performs decodingusing a default schedule. If, at step 606, layered decoder 502 hasconverged on the DCCW, then processing terminates at step 618.Otherwise, layered decoder 502 has converged on a failed codeword, andprocessing proceeds to step 608.

If, at step 608, the number b of USCs in the failed codeword exceeds apre-defined threshold b_(max), e.g., 16, then the codeword is an invalidcodeword, and process 600 terminates at step 618. If, instead, at step608, the value of b is less than or equal to b_(max), then the codewordis an NCW, and processing proceeds to step 610. Note that, if b=0, thenthe NCW is a near-codeword mis-correction (NCW-MC), i.e., the NCWcomprises no USCs, but instead comprises one or more mis-satisfied check(MSC) nodes.

At step 610, process 600 requests the next schedule from schedule set506, where the schedule requested is different from all previouslyselected schedules, including the default schedule. Next, at step 612,if there are no more schedules to be selected, i.e., the schedulerequest of step 610 failed, then processing terminates at step 618. If,instead, at step 612, another matching schedule is available, thenprocessing proceeds to step 614 where the selected schedule is loadedinto layered decoder 502 and decoding, i.e., process 400 of FIG. 4, isre-performed.

If, at step 616, decoder 502 has converged on the DCCW, then process 600terminates at step 618. Otherwise, processing loops back to step 610where a next schedule is selected from the schedule set.

A typical decoder (e.g., layered decoder 502 of FIG. 5) has limitedresources, e.g., memory, clock cycles, etc., and can store only a smallnumber (e.g., 100) of standard schedules in a schedule memory. Sincethere are an infinite number of non-standard schedules, storing allnon-standard schedules in schedule memory is impossible.

An n-layer decoder has n! standard schedules. A typical layered decoderhas anywhere from 3 to 128 layers. A 4-layer decoder has only 24standard schedules, but a 10-layer decoder has over 3.6 million standardschedules, and a 15-layer decoder has over 1.3 trillion standardschedules. For all but a few layered decoders, storing all standardschedules in a schedule memory is impractical.

Thus, key steps in implementing system 500 of FIG. 5 are (i) determiningthe number s of schedules that schedule memory 504 can store and (ii)selecting a schedule set 506 of s schedules to store in the schedulememory. Ideally, the selected schedule set is the set of s scheduleswhich, collectively, successfully decode the largest number of NCWs,i.e., break the largest number of trapping sets.

Successfully decoding NCWs typically involves breaking trapping sets,and trapping sets vary from implementation to implementation, even whenthe same LDPC code is implemented. For example, even if the same LDPCcode is used on two HD drives, the trapping sets associated with the HDdrives may differ. Specifically, trapping sets are influenced by an HDdrive's jitter profile, inter-symbol interference characteristics, andpulse-shaping scheme. These factors can vary not only between HD drivesof different manufacturers, but also between different HD drive modelsfrom the same manufacturer. Thus, a particular standard schedule thatbreaks 12 trapping sets for a particular implementation might break 0trapping sets or 200 trapping sets in another implementation.

Because trapping sets are implementation specific, offline scheduletesting is used to select a schedule set for a particular implementationfrom a set of schedules, i.e., a schedule population. In offlineschedule testing, a particular implementation (e.g., system 100 ofFIG. 1) is simulated in software and/or in a field-programmable gatearray (FPGA). The simulation is then run continuously for a period oftime during which schedules from the schedule population are used todecode near codewords generated by the simulation. The words “simulated”and “production” will be used to distinguish between non-realtimeapparatuses simulated in software or FPGA, e.g., a simulated layereddecoder, and finalized, realtime physical apparatuses, e.g., aproduction layered decoder.

FIG. 7 is a block diagram of a portion of offline schedule-testingsystem 700. System 700 comprises simulated channel 702, simulatedlayered decoder 704, schedule population 706, and hit list 708.Simulated channel 702 simulates the properties of a communicationschannel, e.g., storage medium 110 and channel detector 112 of FIG. 1.Simulated layered decoder 704 simulates the behavior of a layereddecoder, e.g., layered decoder 502 of FIG. 5. Schedule population 706 isa data structure that contains a set of schedules to be tested. Eachschedule in the schedule population has a unique identifier (scheduleID). Hit list 708 is a data structure that records data pertaining tosuccessful decodings.

Simulated channel 702 receives channel input codewords 710 and outputsdecoder-input codewords 712 to simulated layered decoder 704. Simulatedlayered decoder 704 reads schedules 714 from schedule population 706 andwrites data 716 pertaining to successful decodings to hit list 708.

FIG. 8 is a flowchart of offline schedule-testing process 800 executedby simulated layered decoder 704 in system 700 of FIG. 7. Processingbegins at step 802 and proceeds to step 804 where simulated layereddecoder 704 requests a next decoder-input codeword 712 from simulatedchannel 702. If, at step 806, it is determined that the simulation limithas been reached, e.g., a pre-defined limit on the number of codewordsor overall processing time has been exceeded, then processing continuesto step 824 (described below). Otherwise, processing proceeds to step808 where the decoder-input codeword is decoded using a defaultschedule.

Next, at step 810, if simulated layered decoder 704 converged on theDCCW using the default schedule, then processing loops back to step 804where a next decoder-input codeword is requested. If, instead, at step810, the simulated decoder failed to converge on the DCCW and, thus,outputted a failed codeword, then processing continues to step 812,where it is determined whether the number b of USCs in the failedcodeword exceeds a pre-defined threshold b_(max). If b>b_(max), then thefailed codeword is an invalid codeword, and processing loops back tostep 804 where a next decoder-input codeword is requested. If, instead,b≦b_(max), then the failed codeword is a near codeword (NCW), andprocessing continues to step 814 where the next schedule 714 isrequested from schedule population 706.

Next, at step 816, if there are no more schedules in schedule population706, i.e., the request of step 814 failed, then processing loops back tostep 804 where a next decoder-input codeword is requested. Otherwise,processing continues to step 818 where the selected schedule is loadedinto simulated layered decoder 704 and decoding, i.e., process 400 ofFIG. 4, is re-performed. If the simulated layered decoder does notconverge on the DCCW, then, at step 820, processing loops back to step814 where a next schedule is requested from the schedule population.

If, instead, at step 818, the simulated layered decoder does converge onthe DCCW, then, at step 820, processing continues to step 822 where thesuccessful decoding is recorded in hit list 708. Specifically, if no hitcounter exists in the hit list for the current schedule ID, then acounter is created for the current schedule ID in the hit list and thecounter is initialized to 1. If, instead, a counter is found for thecurrent schedule ID in the hit list, then the counter is incremented.

Processing then loops back to step 814 where a next schedule isrequested from schedule population 706.

At step 824, hit list 708 is analyzed and a schedule set is created fora production schedule memory. If the production schedule memory of theactual decoder can store a maximum number s of schedules, then theanalysis at step 824 is to identify the set of s schedules thatsuccessfully decode the greatest number of NCWs. Once the analysis iscomplete, process 800 terminates at step 825.

In offline schedule-testing process 800 of FIG. 8, every generated NCWtypically is tested against every schedule in the schedule population.It is not uncommon to test 10,000 NCWs during offline schedule testing.Simulating on a dedicated computer the decoding of a single NCW with asingle schedule takes approximately 1 second. Thus, to test a singleschedule against 10,000 codewords takes 10,000 seconds, or 2.78 hours. Adecoder with 10 layers (a typical value) has over 3.6 million standardschedules. Testing 3.6 million standard schedules against 10,000codewords using a single computer would take more than 1,140 years. Evenrunning 150 computers simultaneously requires over 7 years of test time.Thus, assuming 10,000 NCWs and n! standard schedules, offlineschedule-testing method 800 of FIG. 8 is impractical for most layereddecoders.

In a failed layered decoder, the layer that contains the largest numberb of unsatisfied check nodes (USCs) is denoted L_(maxb). For example, ifa layered decoder fails, and layer 2 is the layer in the failed decoderthat contains the largest number b of USCs, then L_(maxb)=2. If thereare two or more layers with an equal, greatest b value, then one layermay be selected at random to be L_(maxb).

A triad is a sequence of three layers where no layer is repeated. Thus,[0,1,2] and [8,30,63] are valid triads for a 100-layer code, whereas[0,1] and [63,30,63] are not. Triads are direction specific, e.g., triad[8,30,63] and triad [63,30,8] are two distinct triads. In an n-layercode where n is greater than 2, there are n(n-1)(n-2) triads.

For a given pairing of a standard schedule and an NCW, the layer in thestandard schedule that matches the L_(maxb) value of the NCW is calledthe key layer, and the triad in the standard schedule that contains thekey layer as the middle layer is called the key triad. Thus, if thepairing is a standard schedule [0,1,2,3,4,5] and an NCW with L_(maxb)=2,then layer 2 is the key layer in the standard schedule, and [1,2,3] isthe key triad in the standard schedule.

The ability of a particular standard schedule to successfully decode aparticular NCW is largely a function of the key triad of the standardschedule, and has little to do with the number n of layers in the code,the location of the key triad in the schedule, or the location orsequence of the non-key-triad layers of the standard schedule. Forexample, if a five-layer decoder fails with an NCW where L_(maxb)=2,there is no need to test both standard schedule [4,3,2,1,0] and standardschedule [4,0,3,2,1], because both schedules contain the same key triad[3,2,1], and the location of non-key-triad layers 0 and 4 is more orless irrelevant. Both schedules will be equally successful orunsuccessful in decoding the NCW. The same is true for the otherstandard schedules containing key triad [3,2,1]. Note that scheduleslike [2,1,0,4,3] and [1,4,0,3,2] are also schedules that contain keytriad [3,2,1] because the sequence of layer 3 followed by layer 2followed by layer 1 occurs in two consecutive iterations of each ofthose schedules. In general, it is not necessary to test all n! possiblestandard schedules against a population of NCWs; testing scheduleshaving each of the n(n-1)(n-2) different triads is sufficient.

Triad-Based Population-Selection Methods

Certain embodiments of the present invention are triad-basedpopulation-selection methods for selecting a population of standardschedules of an n-layer code for offline schedule testing, wherein (i)each of the n(n-1)(n-2) triads of the code are present in at least oneschedule in the population and (ii) each schedule is associated with atleast one key-layer value.

In certain triad-based population-selection methods, a separate scheduleis selected and added to the schedule population for each triad. Thus,for example, assume a six-layer decoder with n(n-1)(n-2) or 120 possibletriads. Assume the first triad selected is [0,1,2]. There are (n-2)! or24 schedules that contain the triad [0,1,2], i.e., [0,1,2,3,4,5],[5,0,1,2,3,4], [4,5,0,1,2,3], [3,4,5,0,1,2], [0,1,2,3,5,4],[4,3,0,1,2,5], and so forth. One of the 24 schedules is selected atrandom to be the schedule and added to the schedule population, alongwith a designation of the key layer of the schedule. A next triad isselected, e.g., [0,1,3], and a schedule containing the triad [0,1,3] israndomly selected and added to the schedule population, along with adesignation of the key layer of the schedule. The process is repeateduntil all 120 triads have been exhausted.

In certain other triad-based population-selection methods, a singleschedule in the schedule population might be associated with more thanone triad. For example, the five-layer schedule [0,1,2,3,4] containsfive triads: [0,1,2], [1,2,3], [2,3,4], [3,4,0], [4,0,1]. To generalize,an n-layer standard schedule comprises n unique triads.

Thus, schedule [0,1,2,3,4] is added to the schedule population alongwith five designations linking the schedule to triads [0,1,2], [1,2,3],[2,3,4], [3,4,0], and [4,0,1]. The benefit of this method is that thememory space occupied by the resulting population is considerably less.This method might not alter the total number of decodings to beperformed by offline schedule testing.

Note that a schedule population generated according to triad-basedpopulation-selection methods will include, for every schedule in thepopulation, a designation of the key layer of the schedule, whereas aschedule population generated according to the prior art does not.

Using triad-based population-selection methods to select a schedulepopulation can reduce the number of schedules in the schedule populationfrom the n! schedules of the prior art to n(n-1)(n-2) schedules or evenfewer. The greater the number of layers in the schedule, the greater thereduction. For example, for eight layers, the population drops from40,320 schedules to 336 schedules or fewer. For ten layers, thepopulation drops from 3,628,800 schedules to 720 schedules or fewer.

Layered-Decoding Systems that Select Standard Schedules based onL_(maxb)

Certain embodiments of the present invention are L_(maxb)-basedlayered-decoding systems that, upon converging on a near codeword (NCW)using a first schedule, are adapted to (i) select a second standardschedule, different from the first, from a schedule set, based on theL_(maxb) value of the NCW, (ii) re-perform decoding with the secondschedule, and, optionally, (iii) record to memory (e.g., hit list 708 ofFIG. 7) data pertaining to the decoding performed with the secondstandard schedule. L_(maxb)-based layered-decoding systems can be usedas simulated layered decoders for offline schedule testing (e.g., system700 of FIG. 7) or as production layered decoders for online decoding(e.g., system 500 of FIG. 5).

In offline schedule testing according to certain embodiments of thepresent invention, schedule set 506 is a schedule population generatedby a triad-based population-selection method, i.e., the schedules inschedule set 506 are schedules with an associated key-layer value.

FIG. 9 is a flowchart of offline schedule-testing process 900 executedby simulated layered decoder 704 of system 700 of FIG. 7, wherein theschedules in schedule population 706 are schedules with an associatedkey-layer value, according to various embodiments of the presentinvention. Steps 902, 904, 906, 908, 910, 912, 916, 918, 920, and 926are analogous to steps 802, 804, 806, 808, 810, 812, 816, 818, 820, and826 of FIG. 8.

At step 914, process 900 requests the next schedule from the schedulepopulation where the key layer of the next schedule is equal to layerL_(maxb) for the current NCW.

Out of the n(n-1)(n-2) schedules in the schedule population, only 1/n ofthe schedules have a key layer equal to layer L_(maxb) for the currentNCW, and thus only 1/n of the schedules need to be tested against anyparticular NCW. In other words, only (n-1)(n-2) schedules need to betested against a given NCW. For example, there are 720 schedules for a10-layer decoder. A tenth of the schedules, i.e., 72, have a key layerof 0, another 72 schedules have a key layer of 1, and so forth. Sinceany given NCW contains only one L_(maxb) value, only 72 schedules needto be tested against the NCW.

When combined, the triad-based population-selection method and theL_(maxb)-based layered-decoding system yield significant timeimprovements over the prior-art offline schedule-testing methods.Instead of testing all n! standard schedules against an NCW, certainembodiments of the present invention test only (n-1)(n-2) schedulesagainst an NCW. Thus, for a 10-layer decoder with approximately 3.6million standard schedules and 720 schedules, and assuming 10,000 NCWsto be tested, the time to perform offline schedule testing on a singlecomputer drops from approximately 1,150 years to approximately 200 days.

Step 922 records both the schedule ID and the L_(maxb) key-layer valueto the hit list.

Step 924 takes hit list 708, i.e., the record of successful decodings,and generates a production schedule set that (i) is small enough to bestored within a production schedule memory and (ii) decodes the greatestnumber of NCWs. However, step 924 generates a production schedule setthat comprises not only schedules themselves, but also the key layer(s)associated with the schedules.

In one embodiment of the present invention, step 924 creates a scheduleset using the one-to-one method, where, for every triad, step 924 adds asingle schedule and associates the schedule with a key-layer value. Inother embodiments of the present invention, step 924 generates aschedule set using a more-memory-efficient one-to-many method, wherestep 924 identifies triads, not schedules, that successfully decode themaximum number of NCWs, and then selects the minimum number of schedulesthat contain the most-successful triads. A schedule in a schedule setgenerated by the one-to-many method might be associated with more thanone key-layer value.

The offline schedule-testing embodiment discussed above processes aschedule population of schedules wherein each schedule is associatedwith one or more key-layer values. However, embodiments of the presentinvention are not so limited. It is possible to implement an offlineschedule-testing system according to various embodiments of the presentinvention wherein one or more schedules in the schedule population haveno associated key-layer value. In such an implementation (e.g., system700 of FIG. 7), simulated layered decoder 704 would record to hit list708 not just the key-layer value, but the entire key triad of thecurrent schedule. Upon selecting a new schedule, the layered decoderwould determine the key triad of the selected schedule, and search thehit list to see if the key triad had already been tested against thecurrent NCW. If so, then the current schedule would be dropped andanother schedule selected. If the key triad had not already been testedagainst the current NCW, then decoding would proceed with the selectedschedule, and the results of the decoding recorded to the hit list.

L_(maxb)-based layered-decoding systems can also be used as productionlayered decoders, e.g., system 500 of FIG. 5. In certain embodiments ofthe present invention, schedule set 506 is a schedule set generated byprocess 900 of FIG. 9, i.e., the schedules in the schedule set alreadyhave one or more associated key-layer values.

FIG. 10 is a flow diagram of a layered-decoding method 1000 executed bylayered decoder 502 in production layered-decoding system 500 accordingto various embodiments of the present invention. Steps 1002, 1004, 1006,1008, 1014, 1016, and 1018 are analogous to steps 602, 604, 606, 608,614, 616, and 618 of FIG. 6. Step 1010 selects the next schedule fromschedule set 506 where the key layer associated with the selectedschedule is the same as the L_(maxb) value of the original NCW from step1004. If b=0, i.e., the NCW is an NCW-MC, then any schedule in scheduleset 506 can be selected.

Step 1012 reports no more matching schedules if method 1000 has alreadytried every schedule where the key layer associated with the selectedschedule is the same as the L_(maxb) value of the current NCW. Incontrast, step 612 of FIG. 6 would only report no more schedules ifevery schedule in schedule set 506 had been tried.

In one possible implementation of layered-decoding method 1000, decodingstep 1014 uses the newly selected schedule to re-decode the originalcodeword input to default decoding step 1004. In another possibleimplementation, the re-performance of decoding in step 1014 uses thenewly selected schedule to further decode the NCW from the previousdecoding (i.e., either default decoding step 1004 or the previousexecution of decoding step 1014). In this latter implementation, step1010 selects the next schedule from schedule set 506 where the key layerassociated with the selected schedule is the same as the L_(maxb) valueof the NCW from the previous decoding.

Non-Standard Schedules

The ability of a particular non-standard schedule to successfully decodea particular NCW is largely a function of the frequency of the layerthat matches the L_(maxb) value of the NCW, regardless of the number nof layers in the code or the sequence of the layers in the non-standardschedule. The greater the frequency of layer L_(maxb) in a non-standardcodeword, the greater the probability that the non-standard schedulewill successfully decode the corresponding NCW. For example, if a5-layer decoder fails with an NCW and an L_(maxb) value of 2, then thenon-standard schedule [0,2,1,2,3,2,4,2] will have a greater likelihoodof successfully decoding the NCW than non-standard schedule[4,0,4,3,2,1,0,1] or standard schedule [0,1,2,3,4] because the frequency(i.e., four) of layer 2 in the first schedule is greater than thefrequency (i.e., one) of layer 2 in the second and third schedules.

Thus, in the context of non-standard schedules, the term “key layer”comprises the layer with the greatest frequency. If there are two ormore layers in a non-standard schedule that share the same maximumfrequency value, then one or more of those layers may be selected as keylayers for the schedule. As such, non-standard schedules can be storedin a schedule set and associated with one or more key-layer values.

Furthermore, a non-standard schedule can be tested using offlineschedule-testing methods (e.g., method 800 of FIG. 8), in order todetermine if the non-standard schedule is successful at breakingtrapping sets for NCWs that possess an L_(maxb) value other the value ofthe layer with the maximum frequency. For example, non-standard schedule[0,2,1,2,3,2,4,2] is assumed to have a key-layer value of 2 becauselayer 2 has the highest frequency. However, offline schedule testingmight determine that non-standard schedule [0,2,1,2,3,2,4,2] is alsoeffective at breaking trapping sets in NCWs where L_(maxb)=0. As such,non-standard schedule might be stored in a schedule set and associatedwith both key layer 2 and key layer 0.

Thus, certain embodiments of the present invention are offlineschedule-testing systems (e.g., system 700 of FIG. 7) that associate anon-standard schedule with one or more key-layer values.

Other embodiments of the present invention are decoding systems (e.g.,system 500 of FIG. 5) wherein the default schedule of layered decoder502 is a non-standard schedule.

Yet other embodiments of the present invention are decoding systems(e.g., system 500 of FIG. 5) wherein (i) one or more of the defaultschedule and the schedules in schedule set 506 are non-standardschedules and (ii) layered decoder 502, upon converging on an NCW usinga first schedule, selects a second schedule from schedule set 506, whichsecond schedule is different from all other schedules previously usedduring this local-decoding iteration, and re-performs decoding using thesecond schedule.

Yet other embodiments of the present invention are decoding systems(e.g., system 500 of FIG. 5) wherein (i) schedule set 506 comprises oneor more non-standard schedules, wherein each non-standard schedule isassociated with one or more key-layer values and (ii) layered decoder502 executes a process, e.g., process 1000 of FIG. 10, that selectsnon-standard schedules from schedule set 506 based on the L_(maxb) valueof an NCW.

Standard and Non-Standard Schedules Combined

Since both standard and non-standard schedules can be associated withone or more key-layer values, both types of schedules can be storedtogether in a schedule set according to various embodiments of thepresent inventions.

Thus, certain embodiments of the present invention are offlineschedule-testing systems (e.g., system 700 of FIG. 7) that generateschedule sets that (i) comprise at least one standard schedule and atleast one non-standard schedule and (ii) associate one or more schedulesin the schedule set with one or more key-layer values.

Yet other embodiments of the present invention are decoding systems(e.g., system 500 of FIG. 5) wherein (i) schedule set 506 (A) comprisesat least one standard schedule and at least one non-standard scheduleand (B) associates each schedule with one or more key-layer values and(ii) layered decoder 502 executes a process, e.g., process 1000 of FIG.10, that selects either or both standard and non-standard schedules fromschedule set 506 based on the L_(maxb) value of an NCW.

Although the present invention has been described in the context of harddisk drives and flash drives, the invention is not so limited. Ingeneral, the present invention can be implemented with any systeminvolving communications encoded using an iterative decoder.

Yet further, although embodiments of the present invention have beendescribed in the context of LDPC codes, the present invention is not solimited. Embodiments of the present invention could be implemented forany code which can be defined by a graph, e.g., tornado codes,structured IRA codes, since it is graph-defined codes which suffer fromtrapping sets.

Yet further, although embodiments of the present invention have beendescribed in the context of layered codes wherein each layer comprises aset of check nodes that have no associated bit nodes in common, thepresent invention is not so limited. Embodiments of the presentinvention can be implemented for layered codes where a layer comprises aset of check nodes that have any number of associated bit nodes incommon.

The present invention can be embodied in the form of methods andapparatuses for practicing those methods. The present invention can alsobe embodied in the form of program code embodied in tangible media, suchas magnetic recording media, optical recording media, solid statememory, floppy diskettes, CD-ROMs, hard drives, or any othermachine-readable storage medium, wherein, when the program code isloaded into and executed by a machine, such as a computer, the machinebecomes an apparatus for practicing the invention. The present inventioncan also be embodied in the form of program code, for example, whetherstored in a storage medium or loaded into and/or executed by a machine,wherein, when the program code is loaded into and executed by a machine,such as a computer, the machine becomes an apparatus for practicing theinvention. When implemented on a general-purpose processor, the programcode segments combine with the processor to provide a unique device thatoperates analogously to specific logic circuits.

Unless explicitly stated otherwise, each numerical value and rangeshould be interpreted as being approximate as if the word “about” or“approximately” preceded the value of the value or range.

It will be further understood that various changes in the details,materials, and arrangements of the parts which have been described andillustrated in order to explain the nature of this invention may be madeby those skilled in the art without departing from the scope of theinvention as expressed in the following claims.

The use of figure numbers and/or figure reference labels in the claimsis intended to identify one or more possible embodiments of the claimedsubject matter in order to facilitate the interpretation of the claims.Such use is not to be construed as necessarily limiting the scope ofthose claims to the embodiments shown in the corresponding figures.

It should be understood that the steps of the exemplary methods setforth herein are not necessarily required to be performed in the orderdescribed, and the order of the steps of such methods should beunderstood to be merely exemplary. Likewise, additional steps may beincluded in such methods, and certain steps may be omitted or combined,in methods consistent with various embodiments of the present invention.

Although the elements in the following method claims, if any, arerecited in a particular sequence with corresponding labeling, unless theclaim recitations otherwise imply a particular sequence for implementingsome or all of those elements, those elements are not necessarilyintended to be limited to being implemented in that particular sequence.

Reference herein to “one embodiment” or “an embodiment” means that aparticular feature, structure, or characteristic described in connectionwith the embodiment can be included in at least one embodiment of theinvention. The appearances of the phrase “in one embodiment” in variousplaces in the specification are not necessarily all referring to thesame embodiment, nor are separate or alternative embodiments necessarilymutually exclusive of other embodiments. The same applies to the term“implementation.”

1. A decoder-implemented method for decoding a decoder input codeword,the method comprising: (a) selecting a decoding schedule for layereddecoding, wherein: the layered decoding corresponds to a code having twoor more layers; and at least one layer in the code appears more thanonce in the selected decoding schedule; and (b) performing the layereddecoding on the decoder input codeword using the selected decodingschedule.
 2. The invention of claim 1, wherein the selected decodingschedule cannot be completely decomposed into two or more iterations ofanother decoding schedule in which each layer of code appears.
 3. Theinvention of claim 1, wherein the at least one layer that appears morethan once in the selected decoding schedule corresponds to a layerL_(maxb) in a different decoding schedule used in a previous layereddecoding of the decoder input codeword, wherein the layer L_(maxb) has agreatest number of unsatisfied check nodes (USCs) in a near codeword(NCW) produced during the previous layered decoding.
 4. The invention ofclaim 1, wherein step (a) comprises the step of selecting the subsequentdecoding schedule from a decoding-schedule database comprising aplurality of different decoding schedules, wherein at least one of theplurality of different decoding schedules is associated with at leastone L_(maxb) value.
 5. The invention of claim 4, wherein the associatedL_(maxb) value is a layer that appears most often in the associateddecoding schedule.
 6. The invention of claim 4, wherein the schedules inthe decoding-schedule database are sorted by the number of nearcodewords successfully decoded by each schedule during offlineschedule-testing.
 7. A decoder for decoding a decoder input codeword,the decoder comprising: (a) means for selecting a decoding schedule forlayered decoding, wherein: the layered decoding corresponds to a codehaving two or more layers; and at least one layer in the code appearsmore than once in the selected decoding schedule; and (b) means forperforming the layered decoding on the decoder input codeword using theselected decoding schedule.